Introduction to modern analysis / Shmuel Kantorovitz

This textbook is based on lectures given by the author since 1964 at the advanced undergraduate and graduate levels of Yale University, Chicago University, and Bar Ilan University. The material covers the usual topics of measure theory and functional analysis with applications to probability theory and to the theory of linear partial differential equations.

The book consists of 10 chapters and two applications: 1. Measure, 2. Constructions of measures, 3. Measure and topology, 4. Continuous linear functionals, 5. Duality, 6. Bounded operators, 7. Banach algebras, 8. Hilbert spaces, 9. Integral representations, 10. Unbounded operators. Application I. Probabilities, Application II. Distributions.

The book contains 120 exercises. Some relatively advanced topics are included in each chapter (excluding the first two), for instance, the Riesz-Markov representation theorem, the Haar measure, the von Neumann double commutant theorem, the extension theory for unbounded symmetric operators, the Lyapunov central limit theorem, etc.
The book will be useful for advanced undergraduate and graduate students in mathematics. Bibliography: 75 titles. (Zentralblatt)

Bibliogr. p. [421]-424. Index